Recent radar measurements show that different ground locations respond differently when the polarization of either the receiving or the transmitting antenna is varied (see Dino Guili, "Polarization diversity in radars," Proceedings of the IEEE, Vol. 74, No. 2, February 1986). In 1985, a polarimeter was flown on a NASA aircraft, recording data which were subsequently processed and stored at the Jet Propulsion Laboratory. One difficulty inherent in this experiment was the large storage necessary for each of the images; only a limited number of data sets could be stored. Furthermore, the computer time necessary to synthesize a picture using an arbitrary transmit and receive polarization is mostly devoted to cumbersome data transfers. Clearly, the volume of data needs to be reduced in order to provide the user with a more flexible investigation tool, yet the data volume reduction must not impact the noise level by introducing additional error. Some theoretical concepts will first be presented for clarity and review, as well as a description of the operations necessary to generate a synthetic polarization image from the original data sets. Then two new methods of data compression will be described.